In this work an effcient approach for a-posteriori error estimation
for POD-DEIM reduced nonlinear dynamical systems is introduced. The
considered nonlinear systems may also include time and parameter-affne
linear terms as well as parametrically dependent inputs and outputs.
The reduction process involves a Galerkin projection of the full
system and approximation of the system's nonlinearity by the DEIM
method Chaturantabut & Sorensen (2010). The proposed a-posteriori
error estimator can be effciently decomposed in an offine/online
fashion and is obtained by a one dimensional auxiliary ODE during
reduced simulations. Key elements for effcient online computation
are partial similarity transformations and matrix DEIM approximations
of the nonlinearity Jacobians. The theoretical results are illustrated
by application to an unsteady Burgers equation and a cell apoptosis
model.
%0 Journal Article
%1 wirtz2014aposteriori
%A Wirtz, D.
%A Sorensen, D.C.
%A Haasdonk, B.
%D 2014
%J SIAM J. Sci. Comp.
%K from:mhartmann ians imported vorlaeufig
%N 2
%P A311--A338
%T A-posteriori error estimation for DEIM reduced nonlinear dynamical
systems
%U http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733
%V 36
%X In this work an effcient approach for a-posteriori error estimation
for POD-DEIM reduced nonlinear dynamical systems is introduced. The
considered nonlinear systems may also include time and parameter-affne
linear terms as well as parametrically dependent inputs and outputs.
The reduction process involves a Galerkin projection of the full
system and approximation of the system's nonlinearity by the DEIM
method Chaturantabut & Sorensen (2010). The proposed a-posteriori
error estimator can be effciently decomposed in an offine/online
fashion and is obtained by a one dimensional auxiliary ODE during
reduced simulations. Key elements for effcient online computation
are partial similarity transformations and matrix DEIM approximations
of the nonlinearity Jacobians. The theoretical results are illustrated
by application to an unsteady Burgers equation and a cell apoptosis
model.
@article{wirtz2014aposteriori,
abstract = {In this work an effcient approach for a-posteriori error estimation
for POD-DEIM reduced nonlinear dynamical systems is introduced. The
considered nonlinear systems may also include time and parameter-affne
linear terms as well as parametrically dependent inputs and outputs.
The reduction process involves a Galerkin projection of the full
system and approximation of the system's nonlinearity by the DEIM
method [Chaturantabut & Sorensen (2010)]. The proposed a-posteriori
error estimator can be effciently decomposed in an offine/online
fashion and is obtained by a one dimensional auxiliary ODE during
reduced simulations. Key elements for effcient online computation
are partial similarity transformations and matrix DEIM approximations
of the nonlinearity Jacobians. The theoretical results are illustrated
by application to an unsteady Burgers equation and a cell apoptosis
model.},
added-at = {2018-07-20T10:54:24.000+0200},
author = {Wirtz, D. and Sorensen, D.C. and Haasdonk, B.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2eff43d2c2cc6b2867d4f59fe9b8f70ef/mathematik},
file = {:http\://www.mathematik.uni-stuttgart.de/fak8/ians/publications/files/WSH14_www_WSH12_preprint_version.pdf:PDF},
institution = {University of Stuttgart},
interhash = {e917eea98d0942df7ccfb36441b47b0d},
intrahash = {eff43d2c2cc6b2867d4f59fe9b8f70ef},
journal = {SIAM J. Sci. Comp.},
keywords = {from:mhartmann ians imported vorlaeufig},
number = 2,
owner = {haasdonk},
pages = {A311--A338},
timestamp = {2019-12-18T14:37:55.000+0100},
title = {A-posteriori error estimation for DEIM reduced nonlinear dynamical
systems},
type = {SimTech Preprint},
url = {http://www.simtech.uni-stuttgart.de/publikationen/prints.php?ID=733},
volume = 36,
year = 2014
}